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Closed-form Analytic Maps in One and Two Dimensions Can Simulate Turing Machines

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We show closed-form analytic functions consisting of a finite number of trigonometric terms can simulate Turing machines, with exponential slowdown in one dimension or in real time in two or more. Key words. dynamical systems, universal computation, iterated maps, analytic functions, Halting Problem, Collatz functions, continuous computation, analog computation

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  • Pascal Koiran & Cristopher Moore, 1996. "Closed-form Analytic Maps in One and Two Dimensions Can Simulate Turing Machines," Working Papers 96-06-037, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:96-06-037
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